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There's no indication any offer is forthcoming or Romney would accept it

The meeting comes as Trump speaks to a series of Republicans who opposed his campaign at some point

New York (CNN)President-elect Donald Trump will meet this weekend with one of his fiercest critics: 2012 Republican nominee Mitt Romney, a discussion that could include the position of secretary of state.

The two men are set to discuss "governing moving forward" and potentially a role for Romney in Trump's Cabinet, a senior Republican source told CNN on Thursday.

Romney has long told friends that he would like to serve in government again and the one job he is interested in is secretary of state, a senior Republican with knowledge of the transition tells CNN. The source says that Romney is meeting with Trump in part to discuss it.

The former Massachusetts governor is being presented as a choice that would show Trump is looking for "adults" because he would bring a team of professionals along with him, the source said, adding that the nomination is being seen as a "serious" possibility.

The meeting with Romney comes as concern about Rudy Giuliani's chances of confirmation continue -- a factor, the source said, that has been discussed with Trump. It's also the latest in a series of Trump's conversations and encounters with Republicans who did not support his candidacy in an effort to reunite the GOP following a divisive election that fractured the party establishment.

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Trump is also maintaining a jam-packed schedule Thursday as the President-elect's team looks to tamp down reports of disarray and infighting within the transition effort, which has been slow to ramp up following Trump's shocking victory last week.

One close friend expressed healthy skepticism that Romney would ever serve in the President-elect's Cabinet.

Romney has often talked how his father, George, did not enjoy serving in President Richard Nixon's Cabinet. After McCain won in 2008, Romney told friends that he didn't want to go into McCain's Cabinet, if he won.

"Trump's Cabinet seems like an even lower probability," the friend said. "I wouldn't say never, but I would be surprised."

A Romney appointment would be a startling shift in the two men's relationship.

One former Romney adviser was surprised by the meeting, but said of Romney, "he cares that much. He's a patriot. This isn't about Donald Trump."

Another Romney ally added that the only position that would attract him would be secretary of state. "He's known as the economy guy, but look at his book. He is and was more involved in foreign policy issues. And he was right about everything from ISIS to Russia," the person said.

But on Russia there is major disagreement -- at least in attitude -- between the two men. Romney, during his 2012 campaign, considered Russia an existential threat to the US, while Trump has emphasized the possibility of working closely with Russian President Vladimir Putin. Romney is pro-trade agreements and pro-NATO, while Trump has questioned the US-Europe relationship and campaigned against pacts like NAFTA and the Trans-Pacific Partnership.

Trump repeatedly slammed the former GOP standard bearer during his ultimately successful bid for the a Republican nomination for his defeat to President Barack Obama, describing him in characteristically colorful terms as a failure. Romney returned fire, repeatedly and forcefully arguing that Trump was not qualified to serve as commander-in-chief.

In an eviscerating speech last March, before Trump clinched the Republican nomination, Romney slammed Trump as a "con man," a "phony" and "a fraud."

Romney refused to endorse Trump in the general election. He argued In favor of allowing the Libertarian nominee Gary Johnson onto the debate stage, but did not endorse him either.

Romney also actively sought to recruit a third-party candidate to carry the conservative banner into the 2016 general election and continued to level heated criticism against Trump in the general election.

In a June interview with CNN's Wolf Blitzer, Romney warned that Trump's presidency could usher in "trickle-down racism."

Romney and Trump's meeting will come a week after Romney called to congratulate Trump on his victory, a call Trump tweeted was "very nice!"

Trump's former campaign manager, Kellyanne Conway, said Thursday she believes that Romney and Trump could work together.

"I think what happens with consensus-builders and good negotiators and successful businessmen who know you have to take the counts of many different people, rivals, allies, is that they find a way to work together," she told CNN's Anderson Cooper. "I think it will be a productive conversation."

Packed schedule to show transition is on track

Trump is meeting Thursday with more than a half-dozen potential candidates for top administration posts, Japanese Prime Minister Shinzo Abe and former US Secretary of State Henry Kissinger.

Trump's transition spokesmen also announced Thursday he will name members of the so-called "landing team" of transition officials to work with US officials at the departments of State, Defense Justice and the the National Security Council.

Following the national security landing team announcement Friday, the transition team will also announce early next week the names of individuals who will lead the transition with economic agencies and domestic policy agencies and groups, RNC communications director Sean Spicer said on a conference call with reporters Thursday.

In the eight days since Trump's victory, the President-elect replaced New Jersey Gov. Chris Christie as chairman of the transition with Vice President-elect Mike Pence and a slew of transition officials who worked under Christie were subsequently booted from the transition effort.

Trump is also scheduled to meet with his transition team for two hours on Friday to discuss their progress and go over potential appointments, Trump spokesman Jason Miller said Thursday.

"My transition team, which is working long hours and doing a fantastic job, will be seeing many great candidates today. #MAGA," Trump tweeted.

My transition team, which is working long hours and doing a fantastic job, will be seeing many great candidates today. #MAGA

Miller declined Thursday to provide a timetable for cabinet appointments, stressing that the focus is on "getting it right," rather than an "arbitrary timetable," echoing the comments of Conway.

"In the words of Vice President Biden just yesterday after meeting with Mr. Pence, nobody should expect the government to be formed overnight," Conway said Thursday morning on MSNBC's "Morning Joe." "Nobody is in a rush to do the wrong thing."

Trump will seek ideas on his administration from nine "top shelf people" he is set to meet with Thursday at Trump Tower, some of whom Miller said are "up for cabinet positions" -- though he did not specify which ones.

Trump has announced RNC chairman Reince Priebus as White House chief of staff and his campaign CEO Steve Bannon as chief strategist and senior counselor.

Meetings with Haley, Kissinger, business leaders

As he focuses on filling key national security posts, Trump sought the counsel of 93-year-old former Secretary of State Kissinger. Trump met with Kissinger for a private meeting in May, but the hawkish former secretary of state has also advised Trump's presidential rival Hillary Clinton, who said she "relied on his counsel" during her time helming the State Department.

Trump also met with Nikki Haley, the South Carolina governor who was deeply critical of Trump during the Republican primary, who is under consideration for the secretary of state post and other cabinet positions, according to a transition source.

And continuing with the national security bend of the day, Trump was schedule to speak with Adm. Mike Rogers, the current director of the National Security Agency, and Gen Jack Keane, a retired four star general who advised Clinton in recent years.

The President-elect will also meet with a pair of Fortune 500 CEOs, Oracle's Safra Catz and FedEx's Fred Smith, as well as Cincinnati Mayor Ken Blackwell and Texas Rep. Jeb Hensarling, who is under consideration to helm the Treasury Department.

Shinzo Abe

Trump also met Thursday afternoon in New York with Japanese Prime Minister Shinzo Abe, the first foreign head of state Trump met with in person since becoming president-elect.

The Japanese prime minister told reporters after the meeting that he feels the two leaders will be able to maintain "a relationship of trust."

On the stump, Trump repeatedly argued that Japan should pay a larger share of the costs for US military bases on its soil and even suggested the country should shoulder a greater burden of its defense against the aggressive actions of North Korea and provocations from China.